Model output statistics

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Model Output Statistics (MOS) is a multiple linear regression technique in which predictands, often near-surface quantities, such as 2-meter (AGL) air temperature, horizontal visibility, and wind direction, speed and gusts, are related statistically to one or more predictors. The predictors are typically forecasts from a numerical weather prediction (NWP) model, climatic data, and, if applicable, recent surface observations. Thus, output from NWP models can be transformed by the MOS technique into sensible weather parameters that are familiar to the "person on the street".


Output directly from the NWP model's lowest layer(s) generally is not used by forecasters because the actual physical processes that occur within the Earth's boundary layer are crudely approximated in the model (i.e., physical parameterizations) along with its relatively coarse horizontal resolution. Because of this lack of fidelity and its imperfect initial state, forecasts of near-surface quantities obtained directly from the model are subject to systematic (bias) and random model errors, which tend to grow with time.[1][2]

In the development of MOS equations, past observations and archived NWP model forecast fields are used with a screening regression to determine the 'best' predictors and their coefficients for a particular predictand and forecast time. By using archived model forecast output along with verifying surface observations, the resulting equations implicitly take into account physical effects and processes which the underlying numerical weather prediction model cannot explicitly resolve, resulting in much better forecasts of sensible weather quantities. In addition to correcting systematic errors, MOS can produce reliable probabilities of weather events from a single model run. In contrast, despite the enormous amount of computing resources devoted to generating them, ensemble model forecasts' relative frequency of events—often used as a proxy for probability—do not exhibit useful reliability.[3] Thus, ensemble NWP model output also requires additional post-processing in order to obtain reliable probabilistic forecasts.[4][5]


United States[edit]

MOS was conceived and planning for its use began within the U.S. National Weather Service’s (NWS’s) Techniques Development Laboratory (TDL) in 1965 and forecasts first issued from it in 1968.[6] Since then, TDL, now the Meteorological Development Laboratory (MDL), continued to create, refine and update MOS equation sets as additional NWP models were developed and made operational at the National Meteorological Center (NMC) and then the Environmental Modeling Center or EMC.[7]

Given its multi-decadal history within the U.S. NWS and its continuous improvement and superior skill over direct NWP model output, MOS guidance is still one of the most valuable forecast tools used by forecasters within the agency.[8]

Implementation of MOS guidance[edit]

United States[edit]

Currently there are eight sets of MOS guidance available from MDL, operational and experimental, covering the span of time from the next hour out to 10 days for the United States and most of its territories.[note 1]

Name Update frequency
Localized Aviation MOS Program (LAMP) Every hour
North American Mesoscale (NAM) MOS Twice per day
Short-range Global Forecast System (GFS) MOS Every six hours
Extended-range GFS MOS Twice per day
North American Ensemble Forecast System MOS Twice per day
Short-range ECMWF MOS[note 2] Twice per day
Extended-range ECMWF MOS[note 3] Twice per day
Ensemble ECMWF MOS[note 4] Twice per day

Initially, MOS guidance was developed for airports and other fixed locales where METARs (or similar reports) were routinely issued. Therefore, MOS guidance was and continues to be provided in an alphanumeric 'bulletin' format for these locations. Here is an example of a short-range MOS forecast for Clinton-Sherman Airport, Oklahoma (KCSM) based on the EMC's Global Forecast System model output.

DT /AUG   6/AUG   7                /AUG   8                /AUG   9 
HR   18 21 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 00 06 12 
N/X                    71         101          74         104    72 
TMP  90 96 94 84 78 74 72 84 95100 98 87 82 78 75 88 98102 99 80 73 
DPT  65 62 62 63 63 63 64 65 63 60 60 62 63 63 64 65 63 60 61 63 63 
WDR  21 20 19 16 16 18 19 22 32 07 11 12 16 18 19 22 22 20 20 19 21 
WSP  14 15 13 11 13 10 10 08 06 06 10 08 10 10 10 14 12 15 15 08 07 
P06         2     9     6     1     2     4     2     4     2  6  5 
P12                    14           5           4          10    12 
Q06         0     0     0     0     0     0     0     0     0  0  0 
Q12                     0           0           0           0     0 
T06     29/27 38/21 22/ 6  8/ 2 26/14 24/ 8 16/ 5 12/ 4 27/18 20/ 7 
T12           58/31       24/ 6       39/16       29/ 6    44/25    
CIG   8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8 
VIS   7  7  7  7  7  7  7  7  7  7  7  7  7  7  7  7  7  7  7  7  7 
OBV   N  N  N  N  N  N  N  N  N  N  N  N  N  N  N  N  N  N  N  N  N 

The short-range GFS MOS bulletin is described here.

With the availability of private- and government-owned weather mesonets,[9] new objective analysis and interpolation techniques,[10] gridded GFS MOS guidance became available in 2006.[11][12]

Gridded MOS daytime high temperature over the conterminous United States for 6 August 2014.

Advantages and disadvantages[edit]

The advantage of MOS forecast guidance as developed in the United States allowed for

  • the removal of NWP model bias,
  • prediction of weather elements not forecast by the NWP model, e.g., surface visibilities, cloud ceiling heights,
  • reliable probabilities of binary events, e.g. probability of precipitation and (severe) thunderstorms,
  • reliable probabilities of categorical events, e.g., probability of clear, scattered, broken or overcast skies.

These points, while greatly desired by forecasters, do come at a price. From its very beginnings, the development of robust MOS equations for a particular NWP model required at least two years' worth of archived model output and observations, during which time the NWP model should remain unchanged, or nearly so. This requirement is necessary in order to fully capture the model's error characteristics under a wide variety of meteorological flow regimes for any particular location or region. Extreme meteorological events such as unusual cold- or heat-waves, heavy rain and snowfall, high winds, etc., are important in the development of robust MOS equations. A lengthy model archive has the best chance of capturing such events.

From the 1970s and into the 1980s, this requirement was not very onerous since EMC (then NMC) scientists, being relatively constrained by computational resources at the time, could only make relatively minor, incremental improvements to their NWP models. However, since the 1990s, NWP models have been upgraded more frequently, oftentimes with significant changes in physics and horizontal and vertical grid resolutions.[13][14] Since MOS corrects systematic biases of the NWP model its based on, any changes to the NWP model's error characteristics affects MOS guidance, usually in a negative way.[15][16]

In the case of a major upgrade to a NWP model, the EMC will run the newer version of model in parallel with the operational one for many months to allow for direct comparison of model performance.[17] In addition to parallel real-time runs, EMC also runs the newer model to examine past events and seasons, i.e., retrospective forecasts.

All of these runs from the upgraded model allows the National Weather Service, Weather Prediction Center (WPC), National Hurricane Center (NHC), and Storm Prediction Center (SPC) to evaluate its performance prior to the decision to either accept or reject it for operational use. MDL scientists have taken advantage of these runs to evaluate and reformulate the MOS equations as needed to avoid deterioration in guidance quality.[18]

Other weather centers[edit]

Royal Netherlands Meteorological Institute developed a MOS system to forecast probabilities of (severe) thunderstorms in the Netherlands.[19][20]

Scientists from the Meteorological Service of Canada developed a post-processing system called Updateable MOS (UMOS) that quickly incorporates changes to their regional NWP model without the need for a lengthy model archive.[21] The Canadian UMOS system generates a 2-day forecast of temperatures, wind speed and direction and probability of precipitation (POP). UMOS temperature and wind forecasts are provided at 3-h intervals, and POP at 6-h intervals.

Scientists at the Kongju National University have also implemented a UMOS system to create forecasts of air temperatures over South Korea.[22] It is unclear as to whether it is used operationally at the Korean Meteorological Administration.


  1. ^ Guam and surrounding Northern Mariana Islands only have GFS MOS guidance available
  2. ^ Access to short-range ECMWF MOS is restricted to the NOAA organization
  3. ^ Access to long-range ECMWF MOS is restricted to the NOAA organization
  4. ^ Access to ensemble ECMWF MOS is restricted to the NOAA organization


  1. ^ Lorenz, Edward N. (March 1963). "Deterministic Nonperiodic Flow". Journal of the Atmospheric Sciences. 20 (2): 130–141. Bibcode:1963JAtS...20..130L. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
  2. ^ Simmons, A.J.; Mureau, R.; Petroliagis, T. (1995). "Error growth estimates of predictability from the ECMWF forecasting system". Quart. J. Roy. Meteor. Soc. 121 (527): 1739–1771.
  3. ^ Rudack, David; Ghirardelli, Judy (August 2010). "A Comparative Verification of Localized Aviation Model Output Statistics Program (LAMP) and Numerical Weather Prediction (NWP) Model Forecast of Ceiling Height and Visibility". Weather and Forecasting. 25 (4): 1161–1178. Bibcode:2010WtFor..25.1161R. doi:10.1175/2010WAF2222383.1.
  4. ^ Wilks, Daniel S.; Hamill, Thomas M. (June 2007). "Comparison of Ensemble-MOS Methods Using GFS Reforecasts". Monthly Weather Review. 135 (6): 2379–2390. Bibcode:2007MWRv..135.2379W. doi:10.1175/MWR3402.1.
  5. ^ Veehuis, Bruce (July 2013). "Spread Calibration of Ensemble MOS Forecasts". Monthly Weather Review. 141 (7): 2467–2482. Bibcode:2013MWRv..141.2467V. doi:10.1175/MWR-D-12-00191.1.
  6. ^ Glahn, Harry R.; Dallavalle, J. Paul (January 2000). "TDL Office Note 00-1:MOS-2000" (PDF). Internal publication. Silver Spring Maryland USA: Techniques Development Laboratory: 179. Retrieved 9 August 2014.
  7. ^ Carter, Gary M.; Dallevalle, J. Paul; Glahn, Harry R. (September 1989). "Statistical Forecasts Based on the National Meteorological Center's Numerical Weather Prediction System". Weather and Forecasting. 4 (3): 401–412. Bibcode:1989WtFor...4..401C. doi:10.1175/1520-0434(1989)004<0401:SFBOTN>2.0.CO;2.
  8. ^ Unpublished. "Annual MDL Users Survey 2011" (PDF). pp. 25–27. Retrieved 3 August 2014.
  9. ^ NOAA, Earth Systems Research Laboratory. "MADIS Surface Network Information". Retrieved 7 August 2014.
  10. ^ Glahn, Bob; Im, J.S. (January 2011). "Algorithms for effective objective analysis of surface weather variables". 24th Conf. on Weather and Forecasting/20th Conf. on Numerical Weather Prediction (J19.4). Retrieved 7 August 2014.
  11. ^ Glahn, Bob; Gilbert, Kathryn; Cosgrove, Rebecca; Ruth, David; Sheets, Kari (April 2009). "The Gridding of MOS". Weather and Forecasting. 24 (2): 520–529. Bibcode:2009WtFor..24..520G. doi:10.1175/2008WAF2007080.1.
  12. ^ National Weather Service. "National Digital Guidance Database".
  13. ^ Environmental Modeling Center, Mesoscale Modeling Branch. "Mesoscale Branch Web Page Reference List". Retrieved 7 August 2014.
  14. ^ Environmental Modeling Center, Global Branch. "[GFS/GDAS] Changes since 1991". Retrieved 7 August 2014.
  15. ^ Erickson, Mary C. (March 1991). "Evaluating the Impact of RAFS Changes on the NGM-Based MOS Guidance". Weather and Forecasting. 6 (1): 142–147. Bibcode:1991WtFor...6..142E. doi:10.1175/1520-0434(1991)006<0142:ETIORC>2.0.CO;2.
  16. ^ Erickson, Mary C.; Dallavalle, J. Paul; Carroll, Kevin L. (January 2002). "The new AVN/MRF MOS development and model changes: a volatile mix?". 16th Conference on Probability and Statistics in the Atmospheric Sciences. Retrieved 5 August 2014.
  17. ^ National Centers for Environmental Prediction, Environmental Modeling Center. "EMC Verification Scorecard". Retrieved 12 August 2014.
  18. ^ Antolik, Mark; Baker, Michael (2 June 2009). "On the ability to develop MOS guidance with short dependent samples from an evolving numerical model" (PDF). 23rd Conference Weather Analysis and Forecasting/19th Conference Numerical Prediction. 6A.1. Retrieved 9 August 2014.
  19. ^ Schmeits, Maurice J.; Kok, Kees J.; Vogelezang, Daan H. P. (April 2005). "Probabilistic Forecasting of (Severe) Thunderstorms in the Netherlands Using Model Output Statistics". Weather and Forecasting. 20 (2): 134–148. Bibcode:2005WtFor..20..134S. doi:10.1175/WAF840.1.
  20. ^ van Gastel, Valentijn. "Investigating MSG-SEVIRI data as an additional predictor source in the KNMI probabilistic (severe) thunderstorm forecasting system" (PDF). Koninklijk Nederlands Meteorologisch Instituut. Royal Netherlands Meteorological Institute (KNMI) publication. Retrieved 9 August 2014.
  21. ^ Wilson, Laurence; Vallee, Marcel (April 2002). "The Canadian Updateable Model Output Statistics (UMOS) System: Design and Development Tests". Weather and Forecasting. 17 (2): 206–222. Bibcode:2002WtFor..17..206W. doi:10.1175/1520-0434(2002)017<0206:TCUMOS>2.0.CO;2.
  22. ^ Kang, Jeon-Ho; Suh, Myoung-Seok; Hong, Ki-Ok; Kim, Chansoo (February 2011). "Development of updateable model output statistics (UMOS) system for air temperature over South Korea". Asia-Pacific Journal of the Atmospheric Sciences. 47 (2): 199–211. Bibcode:2011APJAS..47..199K. doi:10.1007/s13143-011-0009-8.

Further reading[edit]

  • Wilks, Daniel S. (2006). Statistical Methods in the Atmospheric Sciences (Second ed.). Academic Press. p. 627. ISBN 0-12-751966-1.